Next, let us consider the wake behind a NACA0012 airfoil with a Gurney flap.
The training data set is prepared using two-dimensional direct numerical simulation at a chord based Reynolds number of \({\rm Re}_c =1000\)  [1]}.
We use 100 snapshots collected over approximately 4 periods for the training of PNN.
For the example of NACA0012 wake, the PNN tries to predict the temporal evolution of fifty POD coefficients for the vorticity field \({\mathbf {a}}^{\iota }=[a^{\iota }_1,a^{\iota }_2, a^{\iota }_{3},...,a^{\iota }_{50}]\)  over 12 time steps \({\mathbf {a}}_t=[{\mathbf {a}}^1,{\mathbf {a}}^2,...,{\mathbf {a}}^{100}]\)  corresponding to approximately a half of vortex shedding period, from the five vorticity sensor measurements on surface of an airfoil at the first instantaneous field \({\mathbf {s}}^1\) .
Hence, the dimensions of input and output are 5 and 600, respectively.
